1. Field of the Invention
The present invention relates to velocity measurement systems and, more particularly, to acoustic Doppler current profilers.
2. Description of the Prior Art
A current profiler is a type of sonar system that is used to remotely measure water velocity over varying ranges. Current profilers are used in freshwater environments such as rivers, lakes and estuaries, as well as in saltwater environments such as the ocean, for studying the effects of current velocities. The measurement of accurate current velocities is important in such diverse fields as weather prediction, biological studies of nutrients, environmental studies of sewage dispersion, and commercial exploration for natural resources, including oil.
Typically, current profilers are used to measure current velocities in a vertical column of water for each depth "cell" of water up to a maximum range, thus producing a "profile" of water velocities. The general profiler system includes a transducer to generate pulses of sound (which when downconverted to human hearing frequencies sound like "pings") that backscatter as echoes from plankton, small particles, and small-scale inhomogeneities in the water. The received sound has a Doppler frequency shift proportionate to the relative velocity between the scatters and the transducer.
The physics for determining a single velocity vector component (v.sub.x) from such a Doppler frequency shift may be concisely stated by the following equation: ##EQU1## In equation (1), c is the velocity of sound in water, about 1500 meters/second. Thus, by knowing the transmitted sound frequency, f.sub.T, and declination angle of the transmitter transducer, .theta., and measuring the received frequency from a single, narrowband pulse, the Doppler frequency shift, f.sub.D, determines one velocity vector component. Relative velocity of the measured horizontal "slice", or depth cell, is determined by subtracting out a measurement of vessel earth reference velocity, v.sub.e. Earth reference velocity can be measured by pinging the ocean bottom whenever it comes within sonar range or by a navigation system such as LORAN or GPS. FIGS. 1a and 1b show example current profiles where North and East current velocities (v.sub.x, v.sub.y) are shown as a function of depth cells.
Commercial current profilers are typically configured as an assembly of four diverging transducers, spaced at 90.degree. azimuth intervals from one another around the electronics housing. This transducer arrangement is known in the technology as the Janus configuration. A three beam system permits measurements of three velocity components, v.sub.x, v.sub.y and v.sub.z (identified respectively as u, v, w in oceanographic literature) under the assumption that currents are uniform in the plane perpendicular to the transducers mutual axis. However, four beams are often used for redundancy and reliability. The current profiler system may be attached to the hull of a vessel, remain on stationary buoys, or be moored to the ocean floor as is a current profiler 100 shown in FIG. 2.
One class of current profilers now in use, so-called "pulse-incoherent" systems, measure mean current profiles over ranges of hundreds of meters. These pulsed sonars use a pulse-to-pulse incoherent method to derive current velocity. Profilers characterized by pulse-incoherent processing use the echoes from each pulse independently, measuring phase changes over a fraction of the pulse duration to determine the Doppler frequency shift, i.e., f.sub.D =.theta./T, where .theta. is a phase change calculated from performing an autocorrelation on a received waveform at an autocorrelation lag T period. To avoid confusion it can be stated that the received signal is coherent during the short lag time over which phase change is detected; the term "incoherent" refers only to the fact that coherence need not be maintained between pulses.
Current profilers are subject to trade-offs among a variety of factors, including maximum profiling range and temporal, spacial (the size of the depth cell), and velocity resolution. Temporal resolution refers to the time required to achieve a velocity estimate with the required degree of accuracy. In typical applications, a current profiler will make a series of measurements which are then averaged together to produce a single velocity estimate with an acceptable level of velocity variance, or squared error.
For many applications, the resulting combination of profiling range and resolution is satisfactory to produce useful results. Often bias is more of a concern than the variance in observations. Bias is the difference between measured velocity and actual velocity. It is caused, for example, by asymmetries in band limiting system components. Measurement bias remains even after long-term averaging has reduced variance to a predetermined acceptable limit. For instance, bias dominance is typically found in measuring large-scale features such as those found at temperature and salinity interfaces.
For other applications, though, the range and resolution of pulse-incoherent systems is inadequate. These applications require the study of oceanic dynamics such as internal waves, small scale turbulence, sharp scale frontal regions delineating jets, meanders, and eddies. Using a visual analogy, the pictures produced of such structures by a pulse-incoherent system are two blurred to be of any use.
The primary limitations of existing pulse-incoherent systems are threefold. First, many seconds or minutes of averaging are required to produce acceptable statistical errors in mean velocity measurement. Second, for traditional applications, depth cell resolution is limited to one meter or greater. Third, small scale turbulence measurement is not possible due to fundamental limitations of incoherent echo processing, namely, because the turbulence produced velocities that change too quickly for the possible combinations of velocity variance and time to average measurements.
Conventional pulse-incoherent systems estimate the Doppler shift from either the pulse change per unit time or the shaft in spectral peak of a single pulse echo. The transmitted waveform is typically a periodic pulse train characterized by a pulse repetition interval (PRI). Thus, to provide for a round-trip visit (including echo time) to the particles, or scatterers, in a given depth cell, the maximum profiling range or depth is one-half the PRI times c. The received echoes are placed in memory bins defined by "time-gating" the receiving signals, i.e., echoes received at time t.sub.n come from scatterers located at a distance 1/2ct.sub.n. The width of the gate is usually matched to the pulse length, T, giving a range resolution of 1/2cT. The velocity (v) of the scatterers in a particular cell is related to the Doppler shift f.sub.D by the following equation: EQU v=1/2.lambda.f.sub.D ( 2)
where .lambda. is the acoustic wavelength (for example, .lambda.=0.5 cm at 300 kHz).
Pulse-incoherent systems are significantly affected by noise. A theoretical lower bound on the variance of the Doppler frequency estimate from a single pulse is given by the Cramer-Rao bound, which for an unbiased estimator is approximated by the following equation for the standard deviation (.sigma..sub.D) of the Doppler frequency: EQU .sigma..sub.D =(2.pi.T).sup.-1 (1+36/SNR+30/SNR.sup.2).sup.1/2( 3)
where SNR is the signal-to-noise ratio of the Doppler shifted echo pulse. Applying equations (2) and (3), the corresponding error (.sigma..sub.r) in the radial velocity (along the beam) estimate is given by the following equation: EQU .sigma..sub.r =1/2.lambda.(2.pi.T).sup.-1 (1+36/SNR+30/SNR.sup.2).sup.1/2( 4)
Therefore, for a given carrier frequency, which depends on the transducer, the minimum velocity error per ping achievable is inversely proportional to the length of the transmitted pulse. It can be shown that the variance, or squared error, grows quadratically toward smaller SNR, and tends to a constant in the limit of zero noise (a large SNR). Thus, conventional pulse-incoherent Doppler systems perform well above an SNR of roughly 10 db where the variance is relatively constant.
Neglecting noise, it is evident that the product of range resolution, 1/2cT, and velocity error per ping, .sigma..sub.r from equation (4), is proportional to the acoustic wavelength, .lambda., and is independent of the pulse length. This range resolution-velocity error trade-off is the most serious limitation of pulse-incoherent systems, and is directly responsible for the widely recognized long averaging times required to control the absolute velocity error.
As an example of averaging time with a pulse-incoherent current profiler consider a 300 kHz carrier frequency profiling over a water column of 300 meters which is measured at depth cells of 1 meter, and pinging twice a second. Further assume a monostatic system wherein the transmitter and receiver circuits share the same transducer. The range resolution of 1 m means that the pulse length T is 1.33 ms. The velocity error per ping can be found from equations (1) and (2) to be about 30 cm/s. To reduce the standard deviation in the estimate of radial velocity to 1 cm/s, requires about 30.sup.2 or 900 pings, which at two pings per second requires that velocity estimates be averaged over about 71/2 minutes.
Pulse-coherent Doppler current profilers have been developed which improve the velocity measurement accuracy over pulse-incoherent current profilers by a factor on the order of 100. These sonar systems profile current velocities over ranges of several meters, but they are seriously limited in application by small velocity dynamic ranges which are ultimately caused by velocity ambiguity effects inherent to pulse-coherent techniques.
For general transmit waveforms, the range-velocity uncertainty (defined by rearranging equation (4) such that the left-hand side of the equation is the product of .sigma..sub.r T) is inversely proportional to the time-bandwidth product of the signal, determined by the signal decorrelation time (e.g., the time that the echo is in the water causing the echo to lose enough energy so that it can not be correlated with itself) and pulse bandwidth. Signal decorrelation time is related to equations (7-9) below as well as to a drop in the SNR due to noise. The basic premise behind the pulse-coherent approach is to increase this product by transmitting a series of short pulses, in which phase coherence is maintained over the transmitted sequence. The time between pulses is adjusted to minimize ping-to-ping interference. A given range cell is ensonified by successive pulses, so that after demodulation, the received signal (sampled by time-gating) is a discrete representation of the Doppler return from that particular range. The Doppler frequency of this signal can then be estimated by a variety of techniques, including spectral analysis, or the "pulse-pair" algorithm (see, e.g., "A Covariance Approach to Spectral Moment Estimation", Kenneth S. Miller and Marvin M. Rochwarger, IEEE Trans. Info. Theory, Sep., 1972).
Velocity error for independent pulse pairs has been analyzed. It can be shown that the pulse pair estimator is a maximum likelihood estimator (i.e., the estimator having the highest probability of being correct), and in the limit of large SNR, the Doppler velocity error per pair is given by the following: EQU .sigma..sub.v =1/2.lambda..sigma..sub.D =2.sup.-3/2 .lambda.B (5)
where B is the Doppler bandwidth in Hz. (2.pi.B).sup.-1 is the decorrelation time, assuming a Gaussian correlation function exp(-1/2(2.pi..tau.B).sup.2) where is time lag. Typical values of B imply an error per root ping (the square root of the variance per number of pings which are included in the average) between 0.1 and 2.5 cm/s, depending on conditions. In the more general case where successive pairs are correlated, the velocity error is a complicated function of pulse spacing, Doppler bandwidth, and the signal to noise ratio.
Since a transmit pulse need only contain a few cycles of the carrier, range resolutions on the order of 5-10 cm are easily attainable (for example, 10 cycles at 300 kHz corresponds to a 2.5 cm pulse length, where the velocity is calculated as c/2 to account for round-trip time). However, despite their outstanding range resolution capabilities, because pulse-coherent systems are sampled, velocities are aliased about the Nyquist frequency of the sampling. This means that samples 2.pi. radians apart in phase are indistinguishable, which leads to the well-known "range-velocity" ambiguity presented in the equation below: EQU R.sub.max V.sub.max =.+-..lambda.c/8 (6)
where R.sub.max is the maximum profiling range of the system and V.sub.max is the maximum velocity resolution. Thus, for a given transmission frequency and desired velocity resolution, a pulse-coherent system is limited in profiling range. Although the ambiguity can be improved by using a non-periodic pulse train, experience has shown that a factor of order five improvement is a practical limit. As a consequence, conventional pulse-coherent systems have been limited to relatively short ranges, of order tens of meters.
As is well-known in the technology, the autocorrelation function is used to measure the dependence of a received waveform at time t with the received waveform delayed by a lag time, and the result is used in calculating the Doppler frequency. In pulse-incoherent Doppler, the correlation time of the signal is primarily determined by the pulse width. Pulse-coherent systems, besides being dependent on pulse width, are also sensitive to various changes in scatterer movement. These phenomenon cause a narrowing of the autocorrelation function, or equivalently, a broadening of the Doppler spectral peak. There are three principal sources of spectral broadening: finite residence time, turbulence within the sample volume, and beam divergence.
With respect to residence time between successive pulses some particles will have moved out of the sample volume while new particles will have been introduced. Since the new particles enter with random phases, the signal will completely decorrelate over a "residence time" of order d/U, where d is a measure of the size of the range cell, and U is the relative velocity between the beam and the scatterers.
Another source of spectral broadening is sample volume turbulence. Turbulent eddies with spatial scales on the order of the sample volume or smaller cause the scatterers to have a distribution of velocities.
Finally, beam divergence contributes to spectral broadening. This effect is analogous to the turbulence broadening except that the diversity in scatterer velocity within the sample volume is caused by the small variation across the beam of the angle between the velocity vector and the normal to the transducer.
The contributions of these three effects to the Doppler spectral broadening can be estimated as follows: EQU B.sub.r =0.2 .vertline.u.vertline./d (7) EQU B.sub.t =2.4 (.epsilon.d).sup.1/3 ( 8) EQU B.sub.d =0.84 sin(.DELTA..theta.)u.sub.c /.lambda. (9)
where d is the half-power scattering volume width, .vertline.u.vertline. is the magnitude of the relative velocity between the beam and the scatters, .epsilon. is the turbulent energy dissipation rate, .DELTA..theta. is the two-way, half-power beamwidth, and u.sub.c is the cross-beam velocity component. The total Doppler bandwidth (B) is the root-mean-square (RMS) of the individual contributions: B=(B.sub.r.sup.2 +B.sub.t.sup.2 +B.sub.d.sup.2).sup.1/2.
In summary, pulse-coherent systems are hampered by a limited profiling range, often just tens of meters. Further, interference between the transmit pulses creates instability: instability to the point where the system produces either very good or very bad velocity measurements with no in-between.
Accordingly, an acoustic Doppler current profiler overcoming limitations such as those described above would readily find application over the entire range of shipboard, fixed-mounted, and moored deployments. Among the possible applications is that of weather prediction wherein the dynamics of cold and warm water mixing remains a difficult and important problem requiring greater spatio-temporal resolutions for large profiling ranges.
In addition, an entirely new set of short spacial and temporal current measurement scales would be made accessible to remote sensing instruments. These measurements include internal waves, small scale turbulence, sharp scale frontal regions, delineating jets, meanders, eddies, and other large scale structures in the ocean. An improved current profiler would achieve a current profiling range comparable to that of existing incoherent acoustic Doppler profilers, but realize a factor of about 100 improvement in the variance of single-pulse velocity estimates.
Lastly, it would be desirable to provide a current profiler with a fast velocity response, i.e., a decrease in averaging time. Such a fast response will improve horizontal spacial resolution if the current profiler is mounted on a moving ship. For example, a current profiler which could average velocity measurements over one-tenth of a mile in the time now required to average over five miles would be a valuable improvement over present technology.